The present work surveys the performance of various widely used density functional theory exchange–correlation (xc) functionals in describing observable surface properties of a total of 27 transition metals with face-centered cubic (fcc), body-centered cubic (bcc), or hexagonal close-packed (hcp) crystallographic structures. A total of 81 low Miller index surfaces were considered employing slab models. Exemplary xc functionals within the three first rungs of Jacob’s ladder were considered, including the Vosko–Wilk–Nusair xc functional within the local density approximation, the Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA), and the Tao–Perdew–Staroverov–Scuseria functional as a meta-GGA functional. Hybrids were excluded in the survey because they are known to fail in properly describing metallic systems. In addition, two variants of PBE were considered, PBE adapted for solids (PBEsol) and revised PBE (RPBE), aimed at improving adsorption energies. Interlayer atomic distances, surface energies, and surface work functions were chosen as the scrutinized properties. A comparison with available experimental data, including single-crystal and polycrystalline values, shows that no xc functional is best at describing all of the surface properties. However, in statistical mean terms the PBEsol xc functional is advised, while PBE is recommended when considering both bulk and surface properties. On the basis of the present results, a discussion of adapting GGA functionals to the treatment of metallic surfaces in an alternative way to meta-GGA or hybrids is provided.

中文翻译：

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埃舍尔（Escher）素描的雅各布梯子（Jacob's Ladder）：评估过渡金属表面特性上广泛使用的密度泛函的性能

本工作调查了各种广泛使用的密度泛函理论交换-相关（xc）泛函在描述总共27种以面心立方（fcc），体心立方（bcc）或六方密堆积（hcp）晶体结构。使用平板模型考虑了总共81个低米勒指数表面。考虑了Jacob梯子的第三个梯级中的示例性xc泛函，包括局部密度近似中的Vosko-Wilk-Nusair xc泛函，广义梯度近似（GGA）中的Perdew-Burke-Ernzerhof（PBE）泛函。 Tao-Perdew-Staroverov-Scuseria功能为meta-GGA功能。混合动力车被排除在调查之外，因为已知混合动力车不能正确描述金属系统。此外，还考虑了PBE的两种变体，即适用于固体的PBE（PBEsol）和改良的PBE（RPBE），旨在提高吸附能。选择层间原子距离，表面能和表面功函数作为详细性能。与可用的实验数据（包括单晶和多晶值）进行的比较表明，没有xc功能最能描述所有表面性质。但是，以统计学平均值而言，建议使用PBEsol xc功能，而在考虑体积和表面性质时，建议使用PBE。根据目前的结果，